Twin Peaks: Pilot (1990) [Laura Palmer]: Stabbed repeatedly (off-screen) by her father (Ray Wise), who was possessed by the evil spirit "Bob." (The killer's identity was not actually revealed until several episodes later.) Her body is shown afterwards lying on the lakeshore, wrapped in a plastic sheet, when Jack Nance discovers her, and is shown several more times at the lakeshore and in the morgue during Michael Ontkean's and Kyle MacLachlan's investigations. (Her body was also shown in photos and/or in the morgue in several subsequent episodes.) (There was also an alternate version of the pilot, made as a feature film for European distribution, which revealed the killer to be "Bob" (Frank Silva), a hospital worker rather than a supernatural being.) (Thanks to PortsGuy)

Twin Peaks: Fire Walk with Me (1992) [Laura Palmer]: Stabbed repeatedly by her father (Ray Wise) while he's possessed by the evil spirit "Bob." (The film shows the events that took place before the pilot episode.)

Homage (1996) [Lucy Samuel]: Shot in the chest by Frank Whaley. It's been a long time since I've seen this movie, but I believe that the actual shot was off-screen; her body was shown immediately after the shooting at the beginning of the movie, and the rest of the movie showed the events leading up to her murder.

Mother Night (1996) [Helga Noth/Resi Noth]: Playing a dual role as sisters, one sister is killed (off-screen) by Nazi soldiers; we learn of her death when Nick Nolte gets the news. The second sister commits suicide by taking a cyanide capsule after revealing herself as a Soviet spy to Nick. (Thanks to Vincent)

L.A. Doctors: Forty-Eight Minutes (1999) [Dr. Sarah Church]: Fatally injured in a car accident, she dies of internal bleeding just before a helicopter arrives to take her to the hospital. (Thanks to Johan)

Desperate Housewives: Unaired Pilot (2004) [Mary Alice Young]: In the original, unbroadcast version of the premiere episode, Sheryl commits suicide by shooting herself, but continues narrating the episode from beyond the grave; after this unused pilot was filmed, she was replaced by Brenda Strong for the actual series. (Thanks to PortsGuy)